Turning to FIG. 1, a conventional transmitter 100 can be seen. In operation, the transmitter 100 is able to convert the baseband signal BB to radio frequency (RF) so as to be transmitted over the transmit circuitry. As part of the conversion process, the transmit processor 102 can perform crest factor reduction (CFR), digital upconversion, DPD, and other processes on the baseband signal BB in the digital domain so as to generate digital I and Q signals. These digital I and Q signals are then converted to analog I and Q signals by digital-to-analog converters (DACs) 104-1 and 104-2 so as to generate analog signals for the modulator (i.e., mixers 108-1 and 108-2 and phase adjuster 110-1 that receives a local oscillator signal by local oscillator (LO) 112). The modulator then generates the RF signal for power amplifier (PA) 114. This PA 114, however, is nonlinear, so the transmit processor's 102 DPD correction allows for the signal to be predistorted in baseband to compensate for nonlinearities in the PA 114.
To perform this DPD correction, transmit processor employs a feedback system, namely feedback circuitry. The feedback circuitry generally comprises analog-to-digital converters (ADCs) 106-1 and 106-2 and a demodulator (which includes mixers 108-3 and 108-4 and phase adjuster 110-2 that receives a local oscillator signal from LO 112). Typically, the demodulator is able to demodulate the RF output from the PA 114 to generate analog I and Q feedback signals, which are then converted to digital I and Q signals by ADCs 106-1 and 106-2.
Turning to FIGS. 2 and 4, examples of the transmit processor 102-1 can be seen in greater detail. As shown, the transmit processor 102-1 (for FIG. 2) or 102-2 (for FIG. 4) generally includes baseband circuitry 202 (which can perform CFR and as well as other tasks), a DPD module 204 (which can either be hardware or software embodied on a processor and memory and which performs the DPD correction), transmit interface 206 (which provides the digital and Q transmit signals to the transmit circuitry), feedback interface 208 (which receives digital I and Q feedback signals from the feedback circuitry), and a filter 210-1 (for FIG. 2) or 210-2 (for FIG. 4). Generally, because there are differences between the mixers 108-3 and 108-4 (as well as other circuitry), there is usually a mismatch between the I and Q paths, and filter 210-1 or 210-4 is intended to compensate for this mismatch. Additionally, for these examples it can be assumed that any IQ mismatch in the transmit path has been corrected or that an image in the transmit path is outside of the band-of-interest.
Looking first to filter 210-1, the filtering scheme is inadequate. The aligned feedback signal y(n) can be represented as:y(n)=h1(n)*x(n)+h2(n)*x*(n)+v(n),  (1)where x(n) is a reference signal, h1(n) is the time domain channel response of the combined transmit and feedback circuits, h2(n) is the time domain channel response due to the IQ distortion, and v(n) is the measurement error including nonlinearity and noise. Each of these channel responses h1(n) and h2(n) can be easily estimated from measurements data using a least square algorithm, so filter 210-1 can be constructed as follows:z(n)=y(n)+hcorr(n)*y*(n),  (2)where z(n) is the output from filter 210-1 and hcorr(n) is the correction. Specifically, this filter 210-1 attempts to eliminate the conjugate of the reference signal x*(n) (which generally corresponds to an image) in equation (1), so, when equation (1) is substituted into equation (2), equation (2) becomes:z(n)=h1(n)*x(n)+h2(n)*x*(n)+v(n)+hcorr(n)*└h1*(n)*x*(n)+h2*(n)*x(n)+v*(n)┘  (3)Performing a Fourier transform on equation (3), it then becomes:
                                                                                        ⁢                                  {                                      z                    ⁡                                          (                      n                      )                                                        }                                            =                            ⁢                                                                                          H                      1                                        ⁡                                          (                      f                      )                                                        ·                                      X                    ⁡                                          (                      f                      )                                                                      +                                                                            H                      2                                        ⁡                                          (                      f                      )                                                        ·                                                            X                      *                                        ⁡                                          (                                              -                        f                                            )                                                                      +                                  V                  ⁡                                      (                    f                    )                                                  +                                                                                                      ⁢                                                                    H                    corr                                    ⁡                                      (                    f                    )                                                  ⁡                                  [                                                                                                              H                          1                          *                                                ⁡                                                  (                                                      -                            f                                                    )                                                                    ·                                                                        X                          *                                                ⁡                                                  (                                                      -                            f                                                    )                                                                                      +                                                                                            H                          2                          *                                                ⁡                                                  (                                                      -                            f                                                    )                                                                    ·                                              X                        ⁡                                                  (                          f                          )                                                                                      +                                                                  V                        *                                            ⁡                                              (                                                  -                          f                                                )                                                                              ]                                                                                                        =                            ⁢                                                                    [                                                                                            H                          1                                                ⁡                                                  (                          f                          )                                                                    +                                                                        H                          2                          *                                                ⁡                                                  (                                                      -                            f                                                    )                                                                                      ]                                    ·                                      X                    ⁡                                          (                      f                      )                                                                      +                                                      [                                                                                            H                          2                                                ⁡                                                  (                          f                          )                                                                    +                                                                                                    H                            1                            *                                                    ⁡                                                      (                                                          -                              f                                                        )                                                                          ·                                                                              H                            corr                                                    ⁡                                                      (                            f                            )                                                                                                                ]                                    ·                                                                                                                      ⁢                                                                    X                    *                                    ⁡                                      (                                          -                      f                                        )                                                  +                                  V                  ⁡                                      (                    f                    )                                                  +                                                                            H                      corr                                        ⁡                                          (                      f                      )                                                        ·                                                            V                      *                                        ⁡                                          (                                              -                        f                                            )                                                                                                                              (        4        )            and the optimal solution to get ride of the image signal X*(−f) is:
                                          H            corr                    ⁡                      (            f            )                          =                              -                                          H                2                            ⁡                              (                f                )                                                                        H              1              *                        ⁡                          (                              -                f                            )                                                          (        5        )            Thus, the correction hcorr(n) is:
                                                        h              corr                        ⁡                          (              n              )                                =                                                                                      -                  1                                            ⁢                              {                                                      -                                                                  H                        2                                            ⁡                                              (                        f                        )                                                                                                                        H                      1                      *                                        ⁡                                          (                                              -                        f                                            )                                                                      }                                      ≈                                                          _                            ·                                                -                                                            H                      2                                        ⁡                                          (                      f                      )                                                                                                            H                    1                    *                                    ⁡                                      (                                          -                      f                                        )                                                                                      ,                            (        6        )            where  is the inverse discrete Fourier transform matrix. When this filter 210-1, however, is applied (for example) to a 6-carrier system, the filter 210-1 is ineffective at eliminating or even substantially reducing the image (as shown in FIG. 3). A reason for this error is that the estimation of channel responses h1(n) and h2(n) are inaccurate in the out-of-band region due to a lack of constraints within this region. Additionally, when the inverse discrete Fourier transform matrix  is used, the time domain filter should to match the frequency domain filter for all frequency points, either in-band or out-of-band. In-band frequency points are well defined, but out-of-band frequency points are simply random because no information is available, indicating that filter 210-1 is not generally accurate.
Now turning to filter 210-2 of transmit processor 102-2 of FIG. 4, this filter 210-2, too, is inadequate. For this filter 210-2, it uses the following alternative construction:z(n)=h1*(n)*y(n)−h2(n)*y*(n),  (7)Similar to filter 210-1, filter 210-2 attempts to eliminate the conjugate of the reference signal x*(n) (which generally corresponds to an image X*(−f)) in equation (1); however, this approach does not employ the use of a correction (i.e., hcorr(n)). When this filter 210-1, however, is applied (for example) to a 6-carrier system, the filter 210-2 is effective at reducing the image (as shown in FIG. 4), but a substantial out-of-band ripple is introduced.
Thus, there is a need for an improved IQ compensation filter.
Some other conventional designs are: U.S. Pat. No. 5,644,596; and 6,681,103; PCT Publ. No. WO2002/082673; U.S. patent application Ser. No. 12/648,898; and Anttila et al., “Frequency-selective I/Q mismatch calibration of wideband direct conversion transmitters,” IEEE Trans. Circuits and Systems II (Special Issue on Multifunctional Circuits and Systems for Future Generations of Wireless Communications), vol. 55, pp. 359-363, April 2008.